In set theory and related branches of mathematics, a collection F of subsets of a given set S is called a family of subsets of S, or a family of sets over S. More generally, a collection of any sets whatsoever is called a family of sets.
The term "collection" is used here because, in some contexts, a family of sets may be allowed to contain repeated copies of any given member, and in other contexts it may form a proper class rather than a set.
Read more about Family Of Sets: Examples, Properties, Hall's Marriage Theorem, Related Concepts
Famous quotes containing the words family of, family and/or sets:
“The same dreadful set,
the same family of orange and pink faces
carved and dressed up like puppets
who wait for their jaws to open and shut.”
—Anne Sexton (1928–1974)
“One banquet in a rich family could feed a poor man’s family for half a year.”
—Chinese proverb.
“To the extent to which genius can be conjoined with a merely good human being, Haydn possessed genius. He never exceeds the limits that morality sets for the intellect; he only composes music which has “no past.””
—Friedrich Nietzsche (1844–1900)